Download the complete pattern of ocular dominance stripes in the striate cortex

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0 Society
for Neuroscience
Printed
in U.S.A.
The Journal
of Neuroscience
Vol. 5, No. 2, pp. 486-501
February
1985
THE COMPLETE
PATTERN
OF OCULAR
DOMINANCE
THE STRIATE
CORTEX
AND VISUAL
FIELD
OF THE
MONKEY’
S. LEVAY,*,’
* Department
M.
CONNOLLY,S3
of Neurobiology,
J. HOUDE,$
AND
STRIPES
MACAQUE
IN
D. C. VAN ESSEN$
Harvard Medical School, Boston, Massachusetts 02115, and $ Division
Institute of Technology, Pasadena, California 91125
of Biology, California
Received April 26, 1984; Accepted July 19, 1984
Abstract
Ocular dominance stripes in the striate cortex of a macaque monkey were labeled by autoradiography
after
injection of [3H]proline
into one eye. The stripes were reconstructed
on a representation
of the flattened
cortical surface by two independent
techniques: one used computer graphics, and the other was the manual
unfolding procedure of Van Essen and Maunsell
(VanEssen, D. C., and J. H. R. Maunsell
(1980) J. Comp.
Neurol. 191: 255-281). The two reconstructions
differed in many details of the pattern but were in agreement
on its general features. As described in earlier studies, the stripes formed a system of parallel bands, with
numerous branches and islands. They were roughly orthogonal
to the Vl/V2 border throughout
the binocular
segment of the cortex. In the lateral part of the operculum, where the fovea is represented, the stripes were
less orderly than elsewhere. In the calcarine fissure the stripes ran directly across the striate cortex from its
dorsal to its ventral margin. In the far periphery the stripes for the ipsilateral
eye became progressively
narrower,
eventually
fragmenting
into small islands at the edge of the monocular
segment. The overall
periodicity
(width of a left- plus right-eye pair of stripes) averaged 0.88 mm but decreased by a factor of about
2 from center to periphery. This decrease was not accounted for solely by shrinkage of the ipsilateral
eye
stripes.
The flattened cortical reconstruction
was transformed back into visual field coordinates, using information
about visual field topography obtained from the detailed mapping study of Van Essen et al. (Van Essen, D. C.,
W. T. Newsome, and J. H. R. Maunsell(1984)
Vision Res. 24: 429-448), as well as from more limited mapping
done in the same monkey that was used for the reconstruction.
In the transformed
map, the stripes increased
in width about 40-fold from the fovea to the far periphery. As deduced previously (LeVay, S., D. H. Hubel, and
T. N. Wiesel (1975) J. Comp. Neurol. 159: 559-576; Hubel, D. H., and D. C., Freeman (1977) Brain Res. 122:
336-343), there were portions of the map in which the stripes followed curves approximating
isoeccentricity
lines, but this relationship
was not very exact or consistent.
The pattern of stripes appears to be more
meaningfully
related to the geometry of the cortical surface. This has significant implications
for understanding
the developmental
mechanisms involved in stripe formation.
The striate cortex (area 17, Vl) is the first major site on the
visual pathway at which information
from the two eyes is
integrated. In many species, geniculocortical
afferents serving
the left and right eyes terminate
in layer 4C as alternating
bands-ocular
dominance stripes. Within a stripe, cells respond
only to stimulation
of the appropriate
eye. By virtue of intracortical projections, which are predominantly
vertical, this eye
dominates the responses of cells in a slab of tissue extended
from pia to white matter-an
ocular dominance column (Hubel
1 We thank R. Leibowitz for histological assistance, M. Peloquin for
photography, K. Tazumi for illustrations, and C. Oto and N. Goodknight for assistance in preparation of the manuscript. This work was
supported by National Institutes of Health Grants EY-ROl-01960 (to
S. L.) and EY-ROl-02091 (to D. C. V. E.)
‘To whom correspondence should be sent, at his present address:
The Salk Institute, P. 0. Box 85800, San Diego, CA 92138.
3 Present address: University of California of Medicine, San Francisco, CA 94143.
and Wiesel, 1968). The present study is aimed at achieving a
detailed description
of the layout of ocular dominance stripes
in the striate cortex of the macaque monkey.
Much is already known about the anatomy of ocular dominance stripes in the macaque. In a large part of striate cortex,
they have a relatively constant width of about 400 pm (Hubel
and Wiesel, 1972). Seen from the cortical surface, the layer 4C
stripes are parallel and often of indefinite length, but there are
numerous branches and isolated segments. There is a general
similarity in the pattern of stripes from one animal to the next,
at least for the part of the cortex that represents the central
15” or so of the visual field (LeVay et al., 1975). For example,
there is a strong tendency for the stripes to meet the margin of
striate cortex (the Vl/V2 border) at right angles.
The method best suited for demonstrating
the complete
layout of ocular dominance
columns is the autoradiographic
detection of [3H]proline
transported
transneuronally
from one
eye (Grafstein, 1971; Hubel et al., 1974a). Although the cortex
is a highly folded structure, a two-dimensional
reconstruction
The Journal
of Neuroscience
Ocular Dominance
of the columns can be obtained, either by manual reconstruction (Van Essen and Maunsell, 1980) or by computerized graphics techniques. We have applied both of these methods in an
attempt to answer several questions about the distribution
of
ocular dominance stripes. First, are there systematic differences, either in their spacing or in the balance between the
eyes, in different regions of area 17? We have found that there
are at least two such differences: a strong dominance of the
contralateral
eye in the periphery of the visual field, and a
significant difference in the average periodicity of the stripes
between the representation
of the vertical meridian and the far
periphery.
Second, what significance should be attached to the actual
pattern formed by the stripes on the cortex? One possibility is
that some orderly relationship
exists between the orientation
of the stripes and the topography of the visual field representation. This possibility has previously been explored by Hubel
and Freeman (1977). They took the partial reconstruction
by
LeVay et al. (1975) and transformed it back onto a map of the
visual field, using information
about field layout and magnification factors available at the time (Daniel and Whitteridge,
1961; Hubel and Wiesel, 1974). They concluded that in much
of the cortex the columns ran close to the representation
of
isoeccentricity
lines. By combining partial physiological
mapping, autoradiography,
and techniques for unfolding the cortex
in the same animal, and by reference to recently published
detailed field maps (Van Essen et al., 1984), we have been able
to make a detailed comparison of the layout of the stripes on
the cortex and their layout in the visual field. We find that the
orientation
of the stripes conforms more closely to the geography of the cortex than to the topography
of the visual
representation,
an observation which may be of significance in
understanding
the formation of this pattern during development.
Materials
and Methods
The bulk of the results presented
in this paper were obtained
from
a single monkey,
a Z-year-old
female crab-eating
macaque
(Mucaca
fa.scicularis),
weighing
1.9 kg. It received two injections,
spaced 4 days
apart, of [3H]proline
into the left eye. Each injection
comprised
2 mCi
of 2,3-[3H]proline
(specific activity,
20 to 40 Ci/mmol)
dissolved in 25
11 of 0.9% NaCl. The injections
were made into the vitreous
with a 27
gauge needle attached
to a length of polyethylene
tubing.
Fourteen
days after the second injection,
the monkey
was prepared
for acute
recording.
It was anesthetized
initially
with ketamine,
followed
by
intravenous
pentobarbitol.
Gallamine
triethiodide
was administered
to
abolish eye movements,
and the monkey
was mechanically
ventilated.
Retinal landmarks
were plotted onto a tangent screen with a reversingbeam opthalmoscope.
Two horizontal
penetrations
were made with a
tungsten microelectrode
into the left striate cortex, close to the midline.
They were aimed so as to pass through
the dorsal and ventral banks of
the calcarine
fissure, as well as the opercular
cortex. Small electrolytic
lesions (5 PA, 5 set, electrode
negative)
were placed at the termination
of each penetration.
At the end of the recording
session the monkey
was perfused
with
10% form01 saline. The left occipital
lobe was divided into two parts
with a horizontal
knife cut. Each part was sunk in 30% sucrose and
frozen sections
were cut in the horizontal
plane. The 20.pm-thick
sections were collected
five to a vial; one section from each vial was
mounted on a gelatinized
slide and processed for autoradiography
using
Kodak
NTB2
emulsion.
After
3 months’
exposure,
the slides were
developed
in Kodak D19. Other
sections were mounted
and stained
with cresyl violet for reconstruction
of the electrode
tracks. The right
hemisphere
(contralateral
to the injected eye) was processed similarly,
except that it was sectioned in a plane tangential
to the center of the
operculum
(the plane used by LeVay et al. (1975) in their reconstruction
using the Liesegang
silver method).
Every autoradiograph
was photographed
at a low power with darkfield illumination.
The photographs
were printed
at a final magnification of X7.6 after correction
for 16% tissue shrinkage
during histological
Stripes
481
processing.
The set of 203 photographs
of the left occipital lobe formed
the basis for the reconstruction
of the columnar
pattern
in this lobe.
Two entirely
independent
methods were used to derive this reconstruction.
The first involved
computer
graphics.
Tracings
were first
made of the labeled patches in layer 4C for each photograph.
Also
included
in the tracings was the Vl/V2
border, wherever
it appeared,
and any places where the electrode
tracks traversed
layer 4C. From
these a second set of tracings
was obtained
in which, by judicious
rotations
and displacements,
all mismatches
between adjacent sections
that had arisen during the mounting
of the sections were eliminated.
The matching
process was performed
separately
for 10 different
segments of striate cortex (operculum,
roof of calcarine
fissure, and so
on). The set of tracings
for each segment
was then entered
in the
computer
by means of a graphics
tablet.
Successive
sections
were
aligned with reference
to the anterior
edge of the block and to the Vl/
V2 border where it appeared
in the sections; the labeled ocular dominance stripes were not themselves
used for alignment.
Once entered
into the computer,
each segment
was rotated
in three-dimensional
space to obtain a surface view and then was photographed.
Segments
with considerable
curvature
were photographed
more than once: for
example,
the operculum
was photographed
from five different
angles.
From each photograph
a tracing
was prepared
in which the labeled
stripes, shown on the computer
screen as stacks of line segments, were
represented by solid bands. For the most part, this filling-in
process
presented
no difficulty,
but in some areas, notably the fovea1 representation where the stripes are highly fragmented
and irregular,
there was
some ambiguity
which had to be resolved subjectively.
The tracings
were then assembled into a complete reconstruction using the pattern
of stripes along the margins of each tracing for purposes of alignment.
Even so, there was sometimes ambiguity in the matching of individual
stripes across the boundaries between segments. It was also necessary
to introduce several relieving cuts around the perimenter
of the reconstruction.
The exact position
of these cuts was arbitrary,
but they were
mainly required
at the two ends of the oval reconstruction
(near the
fovea1 representation
and in the extreme
periphery).
The outline of
this reconstruction,
without
ocular dominance
stripes
included,
is
shown in Figure 1A. Dotted lines in Figure 1A denote the major lines
of folding that exist in ho. The locations
of the six recording
sites are
also indicated
on the map; receptive
field locations
for these sites are
shown in Figure 1B.
The second, manual,
method of reconstruction
has been described
by Van Essen and Maunsell
(1980). In brief, tracings
were made of
layer 4C contours
from sections taken at l-mm intervals.
These contours were then transferred
to a separate sheet, on which they were
aligned with respect
to one another
so as to provide
an accurate
representation
of surface area, with minimal
distortion
of linear relationships.
Figure 1C shows the outline of the resultant
cortical
map,
along with contour
lines from sections at 3-mm intervals,
i.e., every
third contour used in constructing
the map. Dotted lines in Figure 1C
indicate
the medial edge of the operculum
and the major folds of the
calcarine sulcus. The locations of the six recording
sites are also shown.
In order to minimize
distortions,
a single relieving
cut was introduced
in the anterior
portion
of striate cortex, near the fundus of the stem of
the calcarine
sulcus. The magnitudes
of the residual distortions
in the
map were estimated
using the procedure
described
in an earlier study
of striate cortex (Van Essen et al., 1984). Twelve different
regions of
the cortical
surface which were judged to be reasonably
flat and precisely 2 mm on a side were marked
on the section contours
and then
transferred
to the cortical
map, where they are denoted as blackened
compartments
(Fig. 1C). Planimetric
measurements
on these compartments indicate
that there is very little distortion
of surface area (mean,
8%, maximum,
12%). The shear between contours,
as measured by the
angular distortion
of the corners of the compartments,
ranged from 0”
to 25” (mean, 12”), corresponding
to 0 to 10% linear distortion.
Once the manual
version
of the map was completed,
the ocular
dominance
stripes were entered
from each of the 203 section photo
graphs. Registration
betwen sections was achieved by accurate alignment of various landmarks,
such as the points of sharpest curvature
along gyri and sulci, as well as by ensuring
that there was reasonable
alignment
of stripes on neighboring
sections. Each stripe was initially
entered
as a line segment;
segments
from neighboring
sections were
subsequently
filled in to form continuous
stripes. As with the computer
reconstruction,
this process was fairly straightforward,
but there were
many places in which matches had to be made subjectively.
The orientation
of the maps in Figure 1 deserves comment.
We have
488
LeVay
et
al.
Vol.
5, No.
2, Feb.
1985
FLgure 1. Outlines
of the unfolded,
flattened
striate cortex. A, The reconstruction
based on computer
graphics.
Dotted lines indicate
major
sectors of striate cortex which were individually
reconstructed
from face-on viewing angles before being joined. The operculum
is represented
on
the right; various portions
of the calcarine
sulcus are on the left. Locations
of six recording
sites made in two microelectrode
penetrations
are
also shown. B, Receptive
field locations
for recording
sites I to 6 in the striate cortex. C, The manual reconstruction.
Contour
lines are from
sections taken at 3.mm intervals.
Letters (A to F) along the margin indicate
where the contours
of the six sections in Figure 4 (A to F) meet the
border of the striate cortex. Solid squares (“compartments”)
denote regions corresponding
to squares 2 mm on a side in the intact hemisphere.
Each compartment
was identified
by choosing
a 2-mm segment from a smooth region on one section and identifying
a section in which the
corresponding
segment was 2 mm away (including
components
of separation
within
the plane of section as well as between
sections).
The
locations
of these segments
were than transferred
to the cortical
map, and the compartment
was filled in. Locations
of recording
sites are
indicated
in the same manner as for the preceding
map. The separations
between sites differ for the two maps, especially
for sites 4 and 5, mainly
because of foreshortening
along the medial margin of the operculum
in the computer
map.
adopted the convention
that all cortical
maps are illustrated
as though
they were from the right hemisphere,
irrespective
of their hemisphere
of origin.
This convention,
also used in a number
of earlier
studies
(e.g., Van Essen and Maunsell,
1980; Van Essen et al., 1984), results
in the fovea1 representation
of striate cortex always being on the right
side of the map and the inferior
field representation
always on top.
Although
they are by no means identical,
the two maps of striate
cortex are similar
in overall
size and shape. The surface area of the
The Journal
of Neuroscience
Ocular Dominance
manual map was determined
to be 1380 mm*; that of the computer
map is 1050 mm*, a difference
equal to 24% of the manual version.
This discrepancy
is partly attributable
to residual
foreshortening
in
various parts of the computer
map where compensation
for curvature
of the cortical surface was incomplete.
Transformation
from cortex to ui.sual field. To determine
how the
ocular dominance
stripes would appear if projected
onto the visual
field, it is necessary to know the relationship
between cortical
coordinates and visual field coordinates
throughout
the representation.
To
determine
this relationship,
we used information
about the cortical
magnification
factor, as was done by Hubel and Freeman
(1977), except
that we were able to use recently
published
data that provide a more
accurate and complete
analysis of the representation
in striate cortex
(Van Essen et al., 1984). In this study, it was found that the relationship
between
magnification
and eccentricity
can be reasonably
approximated by a modified
power function
of the general form
M.
= a(b + E)-”
(1)
where M. is the area1 magnification
factor (square millimeters
of cortex
per square degree of visual field), E is the eccentricity
and a, b, and x
are adjustable
parameters
which determine
the exact size and shape of
the map and the dependence
of magnification
on eccentricity.
The
specific values of these parameters
were determined
for one hemisphere
that was mapped in detail (a = 103, b = 0.82, x = 2.28), but it was also
shown that there is substantial
individual
variability
in the size, shape,
and internal
organization
of striate cortex and hence in the values of
all three parameters.
In addition,
there are anisotropies
in some parts
of the representation,
such that the linear magnification
factor (millimeters of cortex per degree of visual field) depends on the direction
in
which it is measured.
These anisotropies
are not embodied
in the
simplified
expression
for area1 magnification
shown in equation
1.
We used computer-generated
models that were based on equation
1
(with adjustments
for anisotropies)
to find appropriate
values of the
parameters
for the actual hemisphere
in which the ocular dominance
stripes were mapped. The information
used in making this tit included
the overall size and shape of the cortical map, as well as several pieces
of information
related to its topographic
organization.
The computer
algorithm
for graphically
generating
model representations involved
several computational
stages. First, the visual hemifield was subdivided
into 100 hemi-annuli,
each representing
a narrow
eccentricity
range. Each hemi-annulus
was then divided by radial lines
into 60 compartments.
The transformation
to the cortical
representation was carried out in sequential
fashion by appropriately
magnifying
and transposing
each compartment.
The sequence began at the fovea
and continued
with a full set of compartments
at each eccentricity
range before moving
on to the next eccentricity
range. Each step
involved
taking a compartment
in the visual field, magnifying
it according to the amount
specified by the parametes
being used in conjunction
with equation
1, and positioning
it properly
in relation to the
portion
of the cortical
map already
generated.
One of these steps is
illustrated
schematically
in Figure 2, which shows a compartment
from
the lower visual field and its appropriately
magnified
representation
in
the upper half of the partially
generated
cortical
model (the inversion
reflecting
the known orientation
of the visual representation
in striate
cortex).
For clarity,
the transformation
in Figure
2 is shown for a
compartment
much larger than those actually
used in the algorithm;
their actual size is indicated
for one small region on each map. A key
point in understanding
the algorithm
is that the compartment
under
construction
starts with three of its corners already
determined.
The
coordinates
of the fourth
corner are determined
on the basis of the
total area of the cortical
compartment
and on the presence of any of
the aforementioned
anisotropies
in the linear magnification
factor. The
anisotropies
in the model are produced
by shifting
the fourth corner of
the compartment
by an amount
and direction
that keeps the area
constant
while producing
the desired
ratio of linear magnification
factors along lines of constant
eccentricity
and polar angle (see Figure
2 legend).
The pronounced
curvature
of the vertical
meridian
in Figure 2A is
an intentional
consequence
of the procedure
we used for representing
solid angles in the visual field with minimal
distortion.
A two-dimensional representation
of an intrinsically
curved surface (the visual field
or the retina)
cannot be made without
some type of distortion.
The
algorithm
we chose for mapping
the visual hemifield
is one which
allows a modest degree of shear (angular
distortion)
at high eccentric-
Stripes
489
ities in exchange for no discontinuities
and no stretching
(area1 distortion).
Further
details of the mapping algorithm
will be described elsewhere
(D. C. Van Essen and J. Houde, unpublished
results). For the present
purposes, it is sufficient
to illustrate
the adequacy of the technique
by
showing the final result, a model map, in comparison
to the map from
the actual experimental
hemisphere.
Figure 3 shows the outlines
of
both maps, along with several markers
of visual topography.
In particular, the map of the experimental
hemisphere
(Fig. 3A) shows the
horizontal
meridian
and 10” isoeccentricity
line, determined
from receptive fields of nearby recording
sites, plus the optic disc and monocular crescent representations
determined
from the autoradiographic
results following
the eye injection.
The model map (Fig. 3H) shows the
corresponding
topographic
coordinates.
Obviously,
the two maps are
not identical,
as there were limitations
in the degree to which the
computer
algorithm
could replicate
features such as the curved shape
of the 10” isoeccentricity
line (see Figure 3 legend). The actual parameters of the expression
for area1 magnification
selected for the bestfitting model are given in equation
2 as
M,
= lOO(O.8
+ .)-‘”
(‘3
The resultant
model of striate cortex was encoded in computer
memory
as a set of coordinates
for the vertices of all 6000 compartments
in the
visual fields (x,y space) and a set of coordinates
for the corresponding
compartments in the cortex (u,u space). These data arrays formed the
basis for projecting
ocular dominance
stripes onto the visual field. The
first step was to enter the outlines
of all stripes onto computer
disk
memory
using a grpahics tablet. (The minimum
spacing between data
points correspond to 0.3 mm in the cortex, and the complete set of
stripes was represented by approximately 10” points.) A separate computer program
treated
each data point from the ocular dominance
outline as a pair of U,U coordinates,
identified
the cortical compartment
within which the point was contained,
and determined
the location of
the point relative to the vertices of the compartment. The point was
then assigned visual field (x,y) coordinates
on the basis of this information
about its location
within
an identified
compartment.
Points
belonging
to the same outline were connected
together,
and the resultant back-transformed
stripes were displayed
on a graphics
plotter.
Because of the wide range (50-fold)
in dimensions
of the back-transformed stripes, it was necessary to make several partial plots at different magnifications
and then combine
the images after appropriate
photographic
enlargement.
Other hemispheres.
The right hemisphere
from the main experimental animal was sectioned
tangential
to the opercular
cortex, and photographic
montages
were prepared
of the pattern
of stripes over much
of the operculum
and the roof of the calcarine
fissure. These montages
are in effect planar projections,
and to avoid marked
distortions
they
were not extended
to regions of high curvature.
Besides the one monkey
used for the detailed reconstruction,
several
other monkeys
that had received
eye injections
of [“Hlproline
were
studied. In order to confirm our observations
about the layout of ocular
dominance
stripes in the representation
of the peripheral
visual field,
photographic
montages
of the labeling
pattern
in the roof of the
calcarine
fissure were prepared
from one of these monkeys.
Results
Perhaps on account of the double injection, the transneuronal
labeling was unusually strong in both occipital lobes. As is
usually the case, labeling was heaviest in the representation
of
the far periphery of the visual field and weaker centrally, but
even at the representation
of the fovea stripes, the stripes were
clearly recognizable. The regional differences in density of label
may be related to the fact that there is greater emphasis on
central vision in striate cortex than at the retinal ganglion cell
level (Rolls and Cowey, 1970; Malpeli and Baker, 1975; Van
Essen et al., 1984). Hence, the number of cortical cells to which
each retinal ganglion cell relays its outputs must be larger for
central than for peripheral vision.
Examples of six sections from the horizontally
sectioned set
of autoradiographs
of the left hemisphere
(ipsilateral
to the
injected eye) are shown in Figure 4. Simple inspection of the
autoradiographs
suggested some surprising differences in the
appearance of the stripes in different parts of the cortex. For
490
LeVay et al.
Vol. 5, No. 2, Feb. 1985
B
VISUAL
FIELD
CORTICAL
MODEL
Figure
2. A schematic
diagram of how mathematical
models of the visual representation
in striate cortex were generated.
In this illustration,
each compartment
in the visual field (A) is magnified
according
to the equation
M, a(1 + E)-*, with no anisotropies
or dependence
of
magnification
of polar angle. In the more general case, several types of anisotropy
could be introduced.
One form of anistropy
was a horizontal
“shearing”
between
contours
that produced
an overall tilt of isoeccentricity
lines in a direction
and magnitude
specified by one of the input
parameters.
Another
anisotropy
was a “bending’
of isoeccentricity
contours
that reduced or even reversed their rightward
curvature.
To prevent
oscillations
or other breakdowns
of the algorithm,
it was necessary to start with only minimal
shear or bending for the first few contours
(nearzero eccentricity)
and to build up gradually
to the desired effect at higher eccentricities.
For reasons such as these, the exact mathematical
formulation
for introducing
shear was cumbersome
and will not be detailed
here. The essential
points are: (I) that the actual magnitude
of
shearing and bending can best be assessed by inspecting the graphically displayed cortical model (B) and (2) that all of the shearing and bending
was done in such a way that the area1 magnification was unaffected.
example,
the stripes
stem of the calcarine
seemed
fissure,
to be more closely
spaced
in the
where
the far periphery
is repre-
sented (arrozus in Fig. 4, D and E) than in other parts of the
cortex. Also, there were regions where the labeled patches were
much narrower than the gaps between them (arrow in Fig. 4C),
suggesting an imbalance in the size of ocular dominance stripes
for the two eyes. It was hard to tell, however, just by inspecting
the autoradiographs,
whether these were true regional variations or merely the result of differences in the regularity of the
pattern of stripes or in their orientation
with respect to the
section plane.
There were two regions in which the labeling was continuous
rather than patchy. One was a small, heavily labeled zone in
the roof of the calcarine fissure (Fig. 4B). This was the representation of the optic disc in the contralateral
(noninjected)
eye. The other was a larger, weakly labeled area adjoining the
border of striate cortex far anterior on the dorsal bank of the
calcarine fissure (Fig. 4, C to E). This was the representation
of the contralateral
eye’s monocular crescent. The presence of
some label in this region may be attributed
to leakage of label
across layers in the lateral geniculate nucleus (LGN) (LeVay
et al., 1978).
The labeling pattern in the entire set of sections of the left
hemisphere was entered into the computer (see “Materials
and
Methods”).
This was done separately for 10 different segments
of striate cortex. The reconstructions
of three of these (the
operculum, the roof of the calcarine fissure, and the dorsal
bank of the stem of the fissure) are shown as stereo pairs in
Figure 5. In the figure, each segment has been rotated by the
computer to give an en face view of the columnar pattern. The
opercular segment (Fig. 5A) shows a pattern similar to one that
was prepared previously with the Liesegang silver method
(LeVay et al., 1975). When viewed with stereo glasses, the
pattern
is seen
to be foreshortened
around
the edges,
where
the
cortex curves away from the viewer. For this reason, a total of
five different views of the opercular
segment were photographed. The roof of the calcarine fissure (Fig. 5B) is more
nearly flat. It has two striking features: an elongated region of
continuous label, which is the representation
of the optic disc,
and a region lateral to the optic disc where the labeled bands
(ipsilateral
eye stripes) are clearly much narrower than the
unlabeied gaps (contralateral
eye stripes.) The dorsal bank of
the stem of the fissure (Fig. 5C) contains a region of relatively
narrowly spaced stripes, close to an unlabeled zone which is
part of the monocular
crescent representation
(i.e., the zone
receiving input only from the contralateral
eye).
The surface of the striate cortex contains a significant
amount of intrinsic curvature (i.e., curvature remaining after
unfolding). In Figure 5, A and B, it can be seen that the sign of
the intrinsic curvature is not constant, but rather is pia-outward
for the operculum and pia-inward
for the roof of the calcarine
sulcus. After complete unfolding, but with no tearing, stretching, or shearing, such a surface would have one mound-like
elevated region adjacent to a moderately depressed region,
rather than a simple bathtub-like
appearance. This has been
confirmed using a latex sheet cast over a scale model of a
macaque hemisphere (D. C. Van Essen, unpublished
observations). The existence of this intrinsic curvature is what necessitated the discontinuities
at several places along the margins
of the computer map and the single discontinuity
(coupled with
some internal shear) in the manual version (Fig. 1).
Reconstructions
of the complete pattern of stripes are illustrated in Figure 6. The upper version (Fig. 6A) is from the
computer model, the lower version (Fig. 6B) is from the manual
reconstruction.
In both cases, the reconstruction
is complete
except for a very small region where tissue was damaged during
division of the occipital lobe into two blocks.
Comparing the two versions (which were prepared completely
independently),
it is clear that they differ considerably
from
each other in the details of the pattern of stripes. Some of these
Thx Journal
Ocular Dominance
of Neuroscience
1 cm
Figure 3. Matching
of cortical
maps from the computer
reconstruction (A) and from the mathematically
generated
model (B). The
computer
reconstruction
shows the location
of known
topographic
coordinates,
including
the 10” isoeccentricity
contour,
part of the
horizontal
meridian,
the optic disc (0. D.) representation
(17” eccentricity),
and the monocular
crescent (M. C.; approximately
60” eccentricity).
The mathematical
model includes the same set of topographic
coordinates;
these are approximately
in agreement
with the actual
cortical reconstruction.
differences are distortional
(non-topological)
in nature. In regions where the cortex is nearly flat, the computer version is
probably less distorted than the manual version. This is because
the manual version, while allowing minimal distortion of surface area (see “Materials
and Methods”),
does have significant
angular distortions that result in shearing of the stripe pattern
in places. However, in regions of high curvature or folding, the
manual version is probably more reliable, because the computer
version is subject to foreshortening
and to possible errors in
the joining of segments.
There are also many topological differences between the two
reconstructions.
These must arise from ambiguities
in the
labeling that permitted different decisions as to the locations
of branch points and islands (see “Materials
and Methods”).
We have not attempted to resolve these discrepancies
by a
detailed re-examination
of the original micrographs,
and their
existence clearly limits the reliance that should be placed on
the minute details of the stripe pattern. Again, however, we
believe that the computer version is more accurate in the open
expanses of cortex, and the manual version is more accurate in
the highly curved regions.
In spite of these differences of detail, the two versions are in
agreement on the general layout and appearance of the columns
on the unfolded cortex. There are several features of the pattern
that we wish to point out.
1. In agreement with previous work, the stripes form a
system of parallel bands, with numerous branches and islands.
2. The stripes are roughly orthogonal
to the Vl/V2 border
Stripes
491
throughout
the entire binocular segment of the cortex. This
finding extends observations made in opercular cortex with the
Liesegang silver method (LeVay et al., 1975).
3. On the operculum, the stripes initiating
from the dorsal
and ventral margins of the striate cortex converge and stream
medially. In the lateral and central parts of the operculum,
where the fovea and the first few degrees of the horizontal
meridian are represented, the columns are more disorderly and
fragmented than elsewhere.
4. In the periphery the stripes are arranged in a comparatively simple fashion: they run directly across the map, from
the dorsal to the ventral border of the striate cortex.
5. In the periphery there is a marked imbalance between the
width of the columns for the two eyes. Starting at the lateral
margin of the representation
of the optic disc (i.e., at an
eccentricity of about 20”), the columns for the ipsilateral eye
(the labeled bands in the reconstruction)
become progressively
narrower. By the time one reaches the edge of the monocular
segment, they have fragmented into strings of small islands.
6. The average periodicity,
based on 200 arbitrarily
chosen
sites on the manual reconstruction,
was 0.88 mm/pair (kO.028,
SEM). There is a change in the overall periodicity of the stripes
as one moves from the representation
of central vision to the
far periphery. On the manual version the perimeter of the
entire Vl/V2 border (except the monocular crescent) is 124
mm, along which there are 118 pairs of stripes, for an average
spacing of 1.05 mm/pair. (For the computer version there are
113 pairs in 107 mm.) Considering
only the perimeter of the
operculum, the average width of a left- plus right-eye pair is
1.14 mm. In the cortex, just ventral to the monocular segment
(representing
the superior periphery), a pair of columns averages 0.64 mm in width. Thus, ocular dominance
“hypercolumns” (Hubel and Wiesel, 1974) are almost twice as wide
centrally as in parts of the far periphery. The reduction in their
size in the periphery
is not accounted for entirely by the
reduction in width of the ipsilateral eye’s columns: the contralateral eye columns also become narrower, although to a lesser
extent.
7. There are also local fluctuations
in the periodicity
of
stripes that are not obviously related to visual topography. The
two reconstructions
differ considerably
in this respect: the
manual version (Fig. 6B) shows more local variability
than
does the computer montage (Fig. 6A). The computer version
may underestimate
the variability
in some regions owing to
incomplete correction of foreshortening,
especially along the
margins and in regions of high curvature. The manual version
may include some artifactually
narrow or wide stripes as a
result of incorrect matches or shearing during the unfolding
process. We took some regions that appeared to be accurately
reconstructed in the manual version and re-examined the stripe
width in the original photographs.
From these measurements
and from the photomontage
of the opposite hemisphere
(see
below and Fig. 7), we concluded that local variability (within a
distance of about 10 stripes’ width) was generally quite modest,
with fluctuations
of about 50% being common. Not infrequently, however, 2-fold fluctuations
were encountered,
and
there were occasional but convincing examples of 3-fold differences between nearby stripes. Some of this variability may be
related to the constriction of stripes at branch points (Swindale,
1980). There may also be a tendency for more pronounced
variability
in regions where the cortex is folded. These local
fluctuations,
when coupled with the systematic regional variations noted above, lead to overall extremes of periodicity which
span a 4-fold range: 2.1 versus 0.5 mm/pair averaged over two
pairs of stripes in regions of particularly
narrow spacing (ventral to the monocular crescent) and wide spacing (midway along
the inferior vertical meridian representation).
8. The representation
of the optic disc occupies an elongated
492
LeVay et al.
Figure
4
Vol. 5, No. 2, Feb. 1985
The Journal
of
Neuroscience
Ocular Dominance
Stripes
Figure
5. Stereo pairs of reconstructed
ocular
dominance
stripes
for
three (from a total of eight) segments
of
striate cortex.
The images were photographed
directly
from
the computer
screen, with a 6” angle between
views.
Each segment is viewed en face and with
its pial surface toward
the viewer.
The
scale bar is 1 cm. A, Opercular
segment
(medial is to the left, dorsal is up: same
orientation
as in the final reconstruction
of Fig. 6A). The surface is gently domed
with
a shallow
V-shaped
depression
pointing
laterally.
The perimeter
of the
segment,
except
for the medial
edge,
forms the Vl/V2
border.
This is one of
five views of this segment that were used
in making
the final reconstruction.
B,
Roof of the calcarine
fissure (medial, to
the right; dorsal, up: same orientation
as
in the final reconstruction).
Medially,
this segment
abuts the opercular
segment. None of the perimeter
of this segment forms the Vl/V2
border. The elongated, solidly labeled patch is the representation
of the contralateral
eye’s optic
disc. Lateral
to the disc, the labeled
stripes become narrower
than the gaps
between them. This segment is relatively
flat, except near its edges. The unlabeled
gap running
horizontally
across the entire segment
is the “seam”
between
the
two tissue blocks; due to an error in data
entry, it is represented
at about twice its
proper width. C, Dorsal bank of the calcarine fissure (medial
is to the left; anterior
is down: the segment
is rotated
about 90” counterclockwise
with respect
to its orientation
in the final reconstruction). The left-hand
edge of the segment
forms the Vl/V2
border.
The segment
has a vertically
elongated
depression
toward its right-hand
side (a ripple in the
stem of the calcarine
fissure).
The seam
between
the block
slices through
this
depression
and makes it appear somewhat too deep. The monocular
segment
(dotted region) lies in the sharply curved
base of the fissure.
area, about 7 x 3.5 mm in size, in the roof of the calcarine
fissure. The position of the disc in the retina is known to be on
the horizontal meridian 17” from the fovea (Malpeli and Baker,
1975), which provides an additional
landmark for aligning the
columnar reconstruction
to the map of the visual field. The
disc itself is slightly elongated (7.2” x 5.3”, according to Malpeli
and Baker, 1975) with long axis vertical. The tilt of the long
axis in the cortex with respect to the horizontal
meridian
representation
may reflect the oblique orientation
of isoeccentricity lines in parts of the periphery of the field map (see below
and Fig. 3A). The ocular dominance stripes in the neighborhood
of the disc are not oriented in any special fashion with respect
to it, but merely flow past it.
The right hemisphere of the same brain (contralateral
to the
injected eye) was sectioned tangential
to the center of the
operculum and the roof of the calcarine fissure (see “Materials
and Methods”).
Autoradiographic
montages
were prepared
from these two regions and are illustrated
in Figure 7. On the
operculum
(Fig. 7A) the columns form the familiar pattern,
streaming away from the Vl/VZ border and medially toward
the lip of the calcarine fissure. The labeled and unlabeled bands
are about equally wide throughout
this region. In the roof of
the fissure (Fig. 7B) the optic disc is represented by an unlabeled patch that is once again elongated in shape. Just as was
seen in the left hemisphere,
in the region lateral to the disc,
Figure 4. Six examples
(A to F) from the complete
set of 203 autoradiographs
used in the reconstruction.
They are horizontal
sections through
the occipital
lobe ipsilateral
to the injected
eye. Posterior
is up, medial is to the right. The scale bar is 1 cm. White dots mark the position
of the
border of striate cortex wherever
it appears in the sections. These border crossings
have marked on the cortical
map in Figure 1B. The dorsalmost
and ventralmost
sections (A and F) pass through
the opercular
portion
of striate cortex only; the intervening
sections include both the opercular
region and portions
of the calcarine
fissure. The optic disc of the contralateral
eye is represented
by a small zone of continuous
heavy labeling
in the roof of the calcarine
fissure (arrow
in B). the monocular
crescent is represented
by a larger region of continuous,
weak labeling
on the
dorsal bank of the calcarine
fissure (bottom
center in C, D, and E). Note the regional
variations
in the appearance
of the ocular dominance
patches,
especially
the imbalance
between
the widths
of the labeled and unlabeled
patches in the region between
optic disc and monocular
segment
(e.g., at the arrow in C), and the close spacing of patches in parts of the calcarine
fissure (e.g., arrows in D and E) compared
with the
spacing on the operculum.
494
LeVay et al.
Vol. 5, No. 2, Feb. 1985
1 cm
6. The complete pattern of stripes in the computer reconstruction (A) and the manual reconstruction
reconstructions is the same as in Figure 1, with the operculum to the right and dorsal upward.
Figure
the stripes for the contralateral
eye (in this case the labeled
stripes) are wider than those for the ipsilateral eye.
Since this narrowing
of the ipsilateral eye’s stripes was seen
on both sides of the brain, it seemed unlikely to be an artifact
due, for example, to damage to the injected eye. Even so, given
that this effect had not been described previously, we thought
it possible that it was a peculiarity
of this particular
monkey.
We therefore examined the brains of two other monkeys that
had received eye injections. They both showed the same imbalance in the periphery. Montages of the roof of the calcarine
fissure are illustrated
for one of these monkeys in Figure 8. It
appears, therefore, that the region of cortex carrying the representation
of the portion of the visual field peripheral
to the
optic disc is dominated by input from the contralateral
eye. It
is also apparent from both of these montages that the optic
disc representation
is distinctly elongated, although the recon-
(B). The orientation
of the
structions are not complete enough to determine their precise
dimensions.
Transformation
of stripes onto the visual field. Using recent
data on the topographic
organization
of striate cortex (Van
Essen et al., 1984), in conjunction
with limited mapping data
from the experimental
hemisphere
used in this study, we calculated the complete pattern of stripes, as they would appear
when transposed back to the visual field (see “Materials
and
Methods”).
Figure 9 shows the pattern for the entire pattern
out to 60” eccentricity, which is close to the monocular cresent
(lower inset; see Fig. 9 legend). The pronounced
curvature of
the vertical meridian along the right margin of the map is, as
was described under “Materials
and Methods,”
an intentional
consequence
of the procedure used to construct
a flattened
representation
of the visual hemifield.
There are several interesting
features of these illustrations
that deserve specific mention. Most obvious is the enormous
Figure 7. Photographic
montages
of the ocular dominance
stripes in the hemisphere
contralateral
to the injected eye, prepared
from tangentia
sections.
A, Opercular
segment
(medial
is to the left, dorsal is up). The reconstruction
covers only about 60% of the opercular
surface ant
1s
nowhere
reaches the Vl/V2
border. Some idea of the curvature
of the surface can be gained by inspection
of the “contour
lines”-autoradiograpk
In
were photographed
at lOO-pm intervals.
Compare
with Figure 5A. B, Roof of the calcarine
fissure (same orientation
as A). The reconstructia
does not extend to the medial lip of the fissure. The injected
eye’s optic disc is represented
by an unlabeled
zone medially
(O.D.).
Lateral to tl le
!d
disc the labeled stripes (those for the contralateral
eye) are wider than the gaps between
them. Contrast
this with the pattern
of narrow
labelr
stripes in this region of the opposite hemisphere
(Fig. 5B) and with the equally wide stripes and gaps on the operculum.
Scale bar = 5 mm.
LeVay et al.
Vol. 5, No. 2, Feb. 1985
The Journal
of Neuroscience
Ocular Dominance
Stripes
497
Figure .Y The complete
pattern
of ocular dominance
stripes hack-transformed
onto the visual field out to 60” eccentricity.
The optic disc
appears more elongated
than in the actual retina because no correction
was made for the local anisotropy
involved
in its cortical
representation
(see “Discussion”).
The small oval blank region in the far per&he?,
just below the horizontal
meridian,
corresponds
to the artifactual
gap in the
cortical
reconstruction
(Fig. GA; see “Materials
and Methods”).
The ULW~ in the upper left shows the transformation
for the central
4.5”. The
lotr~r left ins& shows the extent of the entire left visual hemifield,
from Polyak
(1957). The cfa&ed lirw shows the extent of the right eye’s field
of view when the dirertion
of gaze is straight
ahead. The stippled region shows the approximate
extent of the true monocular
crescent, in which
the retinal extent of the left eye exceeds that of the right eye. This was based on the perimetry
measurements
on one of us CD. V. E.) with
different
directions
of gaze for the right eye.
LeVay et al.
498
difference in spacing of stripes between the fovea and the visual
periphery. In the center of the fovea (Fig. 9, upper inset) there
are about 8 pairs of stripes/degree,
whereas in the far periphery,
each pair of stripes occupies several degrees. Outside 5” to lo”,
the stripes show a strong tendency to stream in parallel arcs
that spiral inward while progressing
from the inferior to the
superior vertical meridian.
The fact that their course is not
exactly parallel to isoeccentricity
contours is a reflection of the
oblique orientation
of isoeccentricity
contours in regions where
the stripes run approximately
vertically on the map. The actual
misalignment
is even greater than it appears in this illustration,
however, because our computer model did not fully reflect the
asymmetric orientation
of isoeccentricity
lines in the periphery
(see Fig. 3 and “Materials
and Methods”).
A completely accurate back-transformation
would, for example, show a tendency
for stripes starting at 20” eccentricity
to spiral inward to less
than 10” at the superior vertical meridian.
Discussion
This study represents the first successful reconstruction
of
the complete system of ocular dominance
stripes in primate
striate cortex. Our results have in large part confirmed
a
number of previous observations about the stripes, but several
new and unexpected observations have arisen as well.
By using two entirely independent
methods of cortical reconstruction, we have been able to assess the overall validity and
the relative strengths and weaknesses of the different
approaches. The maps are quite similar in overall shape and in
the location of major landmarks,
although
there are some
regions where the differences are significant.
There are also
many topological
differences in terms of the detailed pattern
of stripes throughout
the map. This was unexpected when we
first compared the two maps, but in retrospect it is perhaps not
so surprising.
The overall pattern was determined
from 200
sections, most containing
between 30 and 80 labeled stripes,
for an estimated total of more than 10,000 matches between
adjacent sections. Thus, even if 99% of the match-ups between
sections were correct on each map, there would nonetheless be
hundreds of discrepancies between maps.
Throughout
the striate cortex, the ocular dominance columns
occur as alternating
stripes, but there are significant
regional
variations in their dimensions
and orientation.
Some of these
variations appear to be largely random, but others are systematically related to the location in the cortex. Thus, the average
periodicity
is significantly
less in the far periphery than more
centrally, but this is superimposed
on local fluctuations
in
periodicity
that are up to severalfold in magnitude. A related
finding by Livingstone
and Hubel (1984) is that the density of
cytochrome oxidase patches increases moderately with eccentricity, from 4.5/mm2 at 0” to 6.5/mm2 at 8”.
We have confirmed previous reports (Kennedy et al., 1975;
LeVay et al., 1980) that the optic disc representation
in striate
cortex is located in the calcarine sulcus, in the smooth region
directly under the operculum.
Its exact location is variable,
though, which presumably correlates with individual variability
in topographic organization
(Van Essen et al., 1984). The ocular
dominance stripes which adjoin the optic disc representation
do not intersect it at a specific angle; rather, their course seems
largely oblivious of its presence. Thus, it does not appear to be
an organizing
center for stripe formation,
at least in the monkey.
An intriguing
feature of the optic disc representation
is its
elongated shape, which is suggestive of a local anisotropy
in
the cortical magnification
factor. The cortical representation
of the optic is about twice as long as it is wide, whereas the disc
itself is only slightly elongated. It measures about 7” X 5”
according to Malpeli and Baker (1975), and in the particular
monkey used in our study the discs appeared very close to
Vol. 5, No. 2, Feb. 1985
circular on ophthalmoscopic
examination.
One clue as to the
basis of this anisotropy is that Hubel et al. (1974b) reported an
anisotropy
in the representation
within
layer 4C, with the
magnification
factor parallel to ocular dominance stripes being
approximately
twice as large as that perpendicular
to the
stripes. The optic disc can thus be regarded as an enlarged
region of strictly monocular input, but with basically the same
type of anisotropic
organization.
Another clue is that the representation
of the optic disc in
the LGN is also quite elongated, even more than in the cortex,
and the axis of elongation is roughly parallel to isoeccentricity
contours (Connolly and Van Essen, 1984). The greater degree
of elongation
in the LGN is probably related to an encroachment from surrounding
parts of the representation
and a net
reduction in size of the optic disc gap relative to the extent
expected if projection
lines were completely free of distortion
in that region (Malpeli and Baker, 1975). In striate cortex the
expected size of the optic disc representation
about 9 mm*,
based on the magnification
factor in this region (0.3 mm2/deg2,
from equation 2) and the size of the optic disc (30 deg2), which
is an ellipse of 7.2 x 5.3” (Malpeli and Baker, 1975). This is in
good agreement with the measured area of 8.8 mm2 for the
computer map (upon which equation 2 was based) and 14 mm2
for the manual map. Thus, the cortical representation
of the
optic disc does not appear to be grossly perturbed by interactions between the two eyes.
The monocular
crescent provides another region in which
interesting
comparisons can be made of the retinal, geniculate,
and cortical representations.
In the visual field, the monocular
crescent is a large, somewhat asymmetric zone occupying about
25% of the hemifield and with a maximum width about onefifth of its length (Fig. 9, lower inset). In the unfolded maps of
the striate cortex, the monocular crescent is, as expected, much
smaller in relative extent (7 to 8% of total surface area). It is
also much less elongated, having approximately
the shape of
an equilateral
triangle.
This is suggestive of an anisotropy
involving
compression
along isoeccentricity
contours, rather
than the elongation
found for the optic disc. In contrast, the
monocular
crescent representation
in the LGN, as identified
by the region in which ipsilateral
and contralateral
eye layers
do not overlap, is highly elongated, even more so than in the
visual field. However, the extent of this non-overlap
region is
only 4% of total laminar surface area, despite the fact that the
overall emphasis on the visual periphery is greater in the LGN
than in striate cortex (Connolly and Van Essen, 1984). This
suggests that lines of projection may be perturbed in this region,
as alluded to already for the optic disc, and that the true
monocular
crescent in the LGN may be significantly
wider.
Hence, the relationship
between LGN and cortical anisotropy
in this region remains unclear.
Ocular imbalance. The normal imbalance between ipsilateral
and contralateral
eye inputs in the visual periphery was not
explicitly mentioned
in previous studies of ocular dominance
stripes, presumably because it is particularly
obvious, mainly
in the irregularly folded cortex in the anterior calcarine sulcus.
It appears to have been noticed but confused with a deprivation
effect by Swindale et al. (1981).4
There are two obvious possibilities
for explaining
the imbalance of inputs at the cortical level. The first is that the imbalance might reflect a naturally occurring form of visual deprivation, given that the anatomical pattern closely resembles that
seen after experimentally
produced
monocular
deprivation
4 The autoradiographic observations on visually deprived monkeys
by Hubel et al. (1977) and LeVay et al. (1980) were restricted almost
entirely to opercular cortex, and the interpretation of those observations is not affected by the present findings.
The Journal
Ocular Dominance
of Neurosciencr
(Hubel et al., 1977; LeVay et al., 1980). The basis of this
deprivation would be the obstruction of the field of view by the
nose. Because of eye movements, the degree of deprivation
would vary continuously
over an extended eccentricity range
centered at about 45” eccentricity, which is where the obstruction begins when the eyes are directed straight ahead. The
second possibility
is that the imbalance reflects the known
anatomical asymmetry in retinal ganglion cell density between
temporal and nasal retina (Van Buren, 1963; Stone and Johnston, 1981). From Van Buren’s (1963) data on the human retina
(Fig. 36 of Van Buren, 1963), cell densities are symmetrical for
eccentricities less than I!?“, but outside of this range, the nasal
(contralaterally
projecting) retina has approximat,ely twice the
cell density of the temporal (ipsilat,erally projecting)
retina.
The retina imbalance is thus present in the appropriate region
and is quantitatively
sufficient to account for the imbalance
seen at the cortical level. If’ this asymmetry is indeed a contrihuting Pact or, it would imply that differences in the number ot
inputs have the same effect as differences in activity levels in
establishing the relative extent of target areas between rompeting inputs, as has been suggested previously for the cat
(I,rVay et al., 197X).
7’mnq,r,sitiorz to thy ~Gsual fidd. Hubel and Freeman ( 1977)
used information
from an earlier study (Hubel and Wiesel,
1974) for estimating the cortical magnification
factor as a
function of eccentricity. Their equation 1 was an expression
for the in\rerse of the linear magnification
factor
nr ’ = o.o6:~stT;+ 0.109
This can be rearranged to give an explicit
linear magnification
factor, M,,,,
ill,,,,
= 1:,.7(k’
+ l.fi2)-1
(2 I
equation
for the
($1
Since they assumed that the representation
was uniformly
isotropic (outside layer 4C), this expression can be squared LO
give their estimate of the area1 magnification
factor, M,,
M” = Mi(fi
+ IAL?-’
i.5)
The exponent of this power function determines how steeply
the magnitication
factor declines with eccentricity outside the
fovea1 region. A value of precisely -1 for linear magnification
is mathematically
very convenient, because it makes it possihle
to integrate both sides cf the equation and hence to ohtam
explicit expression for distance in the cortex as a hmction of
eccentricity. This is the so-called “logarithmic
conformal” mapping described by Fischer (1973) and Schwartz (1980).
In the present study we obtained an expression for the area1
magnification
factor (equation 2) which had the same exponent
as estimated by Hubel and Freeman (1977) but somewhat lower
values for the other two constants in the equation. In particular,
our estimate was 100 versus 246 for the multiplicative
constant,
a, which determines the overall size of the map, and 0.82 versus
1.62 for the additive constant b, which determines the eccentricity range over which the magnification
factor reaches a
plateau for the fovea, rather than increasing without
limit.
These differences are not enormous, but they do affect several
quantitative conclusions. For example, application
of our computerized modeling algorithm to the Huhel and Freeman (1977)
expression for magnification
leads to a model of striate cortex
with a surface area of 2120 mm’, which is substantially
larger
than any actual striate cortex of M. furcicularis
examined in
the study of Van Essen et al. (1984) (range, 690 to 1560 mm’,
n = 31; Van Essen et al., 1984). This presumably accounts for
their slightly higher estimate of the number of stripes encountered in a traverse of the full eccentricity range (75 left-right
pairs versus our direct counting of slightly fewer than 60).
In a formal sense, the information
content of the pattern of
Stripes
499
back-transformed
stripes is entirely derived f’rom. and thus
contained within, the cortical maps of st ripes (Fig. 6) and visual
topography (Fig. 3). Nonetheless, the t ransl’orlllatioli
provides
a particularly
clear illustration
of several major points about
the cortical representation
of the visual field. Most obvious is
the roughly 40-fold range in the width of’ strirjes between the
fovea and the far periphery. Of course. this is prrdictablr
from
the knowledge that the cortical spacing hetwcen stripes decreases by about a factor of 2 with ec’cent ric,ity, whereas the
linear magnification
factor, based on equation 2, changes 7(ifold hetween 0” and 60”. The visual impression 01 the dif’ference
between center and periphery is even larger, though, hecause
the density of stripes of a given length is invrrsely proportional
to weal. not linpnr magnification,
which spans a MOO-told
range
between extremes of the center and periphrr!.
Anot her feature of’ the track-translorrn~~tiol~
suggests a ~CK.
:sihle psychophysical
correlate of’ tort Icill a~~atonry. ‘I’his is t hex
ocular imbalance favoring c.ontralatrral
o\~‘r il)iilatt~ral inputs
in the visual periphery. The imhalnncr
is C’LIdent only in a
small portion of’ the cortical map hut in H mucl~ Iarg:tlr f’rartion
of the visual field along the horizontal
nleridian and in the
lower quadrant. M. Fable and M. Schmid I pcarsonal (.ommuncation) have measured monocular hvperac,uit> for stat icjnar>
and moving verniers at different posi;ions along the horizontal
meridian in human subjects. They find t hilt it is similar in
nasal and temporal hemrfields out to t hr ol)t ic, NIX. but Iyyorrd
the disc it falls off much more steeply in the na~rl t ban iI1 the
I emporal hemifield. ‘I’he correspondrnce
heat\vetsn t hesr psycho
physical observations
and our present anatc~rnicul rrsults is
consistent with the notion that hyprracGt>
1s limited t)y thr
magnification
of the retinal image in layer -1(’ 01 the cortex
(Barlow, 1981; Crick et al., 1981).
One might also expect to find a I)s~c’hol)h!.sic.al (‘orrelate of
the inward spiraling of’ back-transf’ornleti
stripeh HS they prc,press toward the superior vertical meridian. I’rc~sumably. this
would be manifest,ed by a hias favoring upl)c’r f’italds at central
eccentricities
(up to 10” or 20”) and a reversed bias, I’ilvoring
lower fields, in the periphery. However. any huch bias would be
superimposed upon two other asymmetries: striate cortex IIS(Ially has more surface area devoted to thr lower than to the
upper quadrant and more area to the region of’ the horizontal
meridian than to the vertical meridian (Yan l+sen et al., 1981 I
There is substantial individual \ sriability in all oft hrse c’ort ical
asymmetries, though. and any analysis of psychophysical aspmetries should take such variability into account.
Dwrlopmcntal
significancf’. When large-scale rec’onstruc’tions
of ocular dominance stripes were first obtained (LeVay et al.,
1975), it was suggested that the stripes arose because of a
conflict during development
between two opposing inst ructions. One of these was for both left- and right-tsye af’ferents to
occupy the same cortical area according to a single retinotopic
map, and the other was a force tending to keep the two sets of
afferents separate from each other. The segregating influence
was suggested to be a repulsive force hetween afferents from
different eyes, although it could equally well be an attractive
force between afferents from the same eve. Alternating
bands
arise in this situation because they minimize
the interface
between the two sets for a given degree of interpenetration
(as
compared with other possible configurations
such as islands in
a matrix). The periodicity
of the bands is set by the relative
strengths of the two forces. Attempts to model stripe development on the basis of these or related ideas (van der Malsburg,
1979; Swindale, 1980; Fraser, 1984) have shown that, although
stripes are indeed generated, they show onlv local order. For
the stripes to remain parallel over any considerable extent of
cortex requires the presence of an external, anisotropic ordering
influence. This anisotropy has been suggested to be an elongation of all the geniculocortical
aborizations
in one direction
500
LeVay et al.
(von der Malsburg, 1979), a gradual anisotropic stretching of
the cortex during stripe formation (Swindale, 1980), and/or a
difference in the strength of two orthogonal
gradients of adhesiveness (von der Malsburg, 1979; Fraser, 1984).
These various descriptions for an anisotropic
influence are
not mutually exclusive, and they need not represent fundamentally independent mechanisms. We suggest that this issue can
best be analyzed by first considering a more basic anisotropy,
relating to the boundary conditions
for the geniculocortical
projection. The largest of the LGN layers are roughly circular
in outline (Connolly and Van Essen, 1984), whereas the cortex
is approximately
twice as long as it is wide, with the long axis
oriented horizontally
in our standard format. Thus, to a first
approximation,
it is reasonable to regard the geniculocortical
projection as a problem of mapping two circular discs, one for
each eye, onto a horizontally
elongated ellipse. From a global
standpoint, the simplest way of achieving this is to slice each
disc into thin vertical strips and then to interdigitate
the left
eye and right eye strips, thereby forming an appropriately
elongated ellipse. If, instead, one started with discs cut into
horizontal strips that were stacked vertically, the strips would
have to be stretched horizontally
or shrunk vertically by 4-fold
in order to obtain the requisite elongation. More generally, the
only way to obtain elongation along one axis without anisotropic stretching of the inputs is to interdigitate
strips cut
orthogonal to that axis.
This constitutes a general argument for why one might expect
stripes to run parallel to the axis of compression of the geniculocortical mapping, which also turns out to be the short axis
of the striate cortex. However, the actual determination
of
stripe orientation
during development
must be a process involving local interactions of geniculocortical
terminals and only
indirectly reflecting global constraints. These constraints could
be exerted at a local level by any of several mechanisms
including, but not restricted to, those suggested above.
Initially, inputs from the two eyes form separate, completely
overlapping projections (Rakic, 1976; Hubel et al., 1977; LeVay
et al., 1980), so that the starting condition for ocular segregation
is a pair of asymmetrically
expanded geniculocortical
mappings.
Also, it is likely that segregation involves retraction of initially
overextended arbors of LGN axons (LeVay and Stryker, 1979).
If the global anisotropy is reflected by a corresponding
elongation of the terminal arborizations
of LGN axons, the process
of terminal
retraction
and segregation would tend to form
stripes orthogonal to the axis of elongation (von der Malsburg,
1979).
Why might individual axonal arbors be elongated? One possibility already mentioned is a difference in the strength of two
orthogonal
gradients involved in establishing
topographic
organization in the geniculocortical
projection (von der Malsburg,
1979; Fraser, 1984). The degree of axonal elongation and also
the ease of terminal displacement
would be greater along the
axis of the weaker gradient, thereby leading to stripes parallel
to the stronger gradient. If the two cortical gradients differed
by the same absolute amounts at the two extremes, the gradient
along the short axis would be roughly twice that along the long
axis. Thus, this form of the gradient hypothesis could account
for the actual orientation
of stripes in a way that is related to
the anisotropy in physical dimensions of striate cortex and not
to the anisotropy of the geniculocortical
transformation.
The
same hypothesis might account for the less orderly arrangement
of stripes near the fovea1 representation,
where the outline of
cortex narrows and the gradients might be more isotropic.
A different basis for explaining asymmetries of axonal arborization and subsequent segregation relates to activity patterns
and to anisotropies
in linear magnification
factor in parts of
the visual cortex. Several lines of evidence suggest that stripe
formation is an activity-dependent
process, with the probability
Vol. 5, No. 2, Feb. 1985
of synaptic survival enhanced by synchronous activity (Hubel
and Wiesel, 1965; Blasdel and Pettigrew, 1979; Stryker, 1981;
Meyer, 1984). There is also evidence for correlated firing patterns of neighboring
retinal ganglion cells of like type (Mastronarde, 1983). It is plausible to suppose that the degree of
correlation is dependent on retinal ganglion cell separation in
a radially symmetric fashion, although this has yet to be experimentally
determined.
In striate cortex, however, there are
several regions where the representation
of the visual field is
anisotropic.
In particular,
the representation
of the vertical
meridian is elongated parallel to the striate border both near
the fovea1 representation,
as shown from the ingenious 2deoxyglucose experiments by Tootell et al. (1982), and in the
peripheral representation,
as shown by standard electrophysiological mapping (Van Essen et al., 1984). In these regions,
correlated activity in a circular region of retina would map to
an elongated strip of cortex during the period of binocular
overlap. This could contribute to an initial elongation of terminals parallel to the striate border and subsequently to the
observed segregation into stripes orthogonal
to the border.
Along the horizontal
meridian, the cortical representation
is
close to isotropic (Van Essen et al., 1984), and this might be
related to the less orderly configuration
of stripes in parts of
this region.
Finally, what basis might there be for the various regional
differences in periodicity
of stripes, such as their narrower
spacing in the periphery? As noted above, the periodicity may
be determined
by the relative strength of two forces, one
tending to keep opposite-eye afferents apart and the other
tending to map them onto retinotopically
corresponding
sites.
There are many ways in which either or both of these forces
might vary modestly with eccentricity.
One possibility worth
specific mention is related to the increased emphasis on central
vision in striate cortex relative to that in the LGN (Malpeli
and Baker, 1975; Connolly and Van Essen, 1984). This results
in more LGN afferents per square millimeter in the periphery
relative to the fovea of the striate cortex. Also, the relative
input from magnocellular
versus parvicellular
layers is greater
in the periphery than in fovea1 striate cortex. Such differences
in the density or type of afferent fiber might have a significant
effect on the range of competitive
interactions
during stripe
formation in the cortex.
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